Method for measuring parameters of quartz crystal units and fixture for carrying out the same

ABSTRACT

The present invention discloses a method and fixtures for measuring parameters of quartz crystal units in the very high frequency (VHF) range. A non-reactive frequency and resistance of the crystal unit are determined, a radio-frequency voltage is applied to a series circuit composed of said crystal unit and a circuit which is adjustable to non-reactive resistance, the phase of the terminal voltage across said circuit which is adjustable to non-reactive resistance is adjusted so as to coincide with the phase of the terminal voltage across said series circuit. Next, said crystal unit is replaced by another crystal unit, and the frequency of said radio-frequency voltage is adjusted so that the above-mentioned two phases coincide. Thus the non-reactive frequencies and or resistances of a plurality of crystal units are quickly determined.

Elite States atent 1191 Koga et a1. Aug. 27, 1974 METHOD FOR NEASURINGPARAMETERS 2,602,838 7/1952 13615618116 et al. 324/57 0 OF QUARTZCRYSTAL UNITS AND 2,733,405 1/1956 Gerber 324/56 2,976,604 3/1961Kosowsky 324/56 x FIXTURE FOR CARRYING OUT THE SAME 3,267,373 8/1966Webb 324/81 [75] Inventors: Issac Koga; Shigeo Kobayashi; Isao Okamoto,all of Tokyo, Japan [73] Assignee: Kokusai Dens hiii l erivva liabushikiKaisha, Tokyo, Japan 57] [22] Filed: June 21, 1973 [21] Appl. No.:372,165

[30] Foreign Application Priority Data June 28, 1972 Japan 47-64064 [52]U.S. Cl 324/56, 324/57 Q, 324/81 [51] Int. Cl. G01r 29/22, GOlr 23/00[58] Field of Search 324/56, 57 R, 57 Q, 81

[56] References Cited UNITED STATES PATENTS 2,137,787 11/1938 Snow324/57 R 2,424,249 7/1947 Miller 324/81 X 2,448,581 9/1948 Fair 324/562,476,954 7/1949 Blackburn 324/56 2,542,275 2/1951 Ekstein 324/56 RADIOFREQUENCY Primary ExaminerGerard R. Strecker ABSTRACT The presentinvention discloses a method and fixtures for measuring parameters ofquartz crystal units in the very high frequency (VHF) range. Anon-reactive frequency and resistance of the crystal unit aredetermined, a radio-frequency voltage is applied to a series circuitcomposed of said crystal unit and a circuit which is adjustable tonon-reactive resistance, the phase of the terminal voltage across saidcircuit which is adjustable to non-reactive resistance is adjusted so asto coincide with the phase of the terminal voltage across said seriescircuit. Next, said crystal unit is replaced by another crystal unit,and the frequency of said radio-frequency voltage is adjusted so thatthe above-mentioned two phases coincide. Thus the nonreactivefrequencies and or resistances of a plurality of crystal units arequickly determined.

2 Claims, 13 Drawing Figures SOURCE PHASE METER I PATENTEDAIIBZTIQH I II 3.882.681

SHEET 1 [IF 6 RAD|0 FREQUENCY SOURCE H2 no I020 |O7b HEADLESS ".|O7QSCREW In To v ADJUSTABLE TO RADIO TO v FROM I FREQUENCY OUTSIDE SOURCEI01 PATENTED 3832.631

SHEET 2 0F 6 PROBE-TI P Fig. C

INSULATOR PATENTEB 15271974 3. 8-32. 531

SHEET '4 BF 8 W CRYSTAL UNIT r 4 SHORT CIRCUI PIECE Hg 5 I NOMINALFREQUENCY OF CRYSTAL UNIT NoIvIINAL FREQUENCY OF CRYSTAL UNITPATENTEDAUGZHQH SHEET 5 OF 5 ELEVATED KFREQUENCY AXIS a E a A DI E C EDu PATENTEU AUB27|974 39832963 1 WEE 8 BF 6 ADJUSTABLE RO OUT METHOD FORMEASURING PARAMETERS OF QUARTZ CRYSTAL UNITS AND FIXTURE FOR CARRYINGOUT THE SAME The present invention relates to a method and some fixturesfor simply measuring parameters of quartz crystal units and especiallyfor simply and precisely measuring the non-reactive frequency andresistance of a quartz crystal unit in a very high frequency (VHF)range. Herein, non-reactive frequency and resistance are frequency andresistance respectively when the impedance of a crystal unit becomesnon-reactive.

Measuring parameters of a quartz crystal unit, especially measuringprecisely the frequency of a quartz crystal unit is very important, andvarious measuring methods are used in European countries and America.Recently, a precise measurement for VHF crystals is required. However,based on careful investigation by the inventors it has been found thatthe measuring principles and circuits, which are now actually used arenot satisfactory even when an operating frequency is not very high,because of stray inductances and capacitances existing in between thecircuit elements including lead wires.

An object of the present invention is to provide a method and somefixtures which can effect a sufficiently accurate measurement by dulygetting rid of the effect of the above-mentioned stray inductances andcapacitances even in the VHF range.

Further features and advantages of the present invention will beapparent from the ensuing description with reference to the accompanyingdrawings to which, however, the scope of the invention is in no waylimited.

FIG. 1A is a circuit diagram explaining the principle of the presentinvention, and

FIG. 1B shows a fixture for carrying out the method according to thepresent invention using the circuit diagram shown in FIG. 1A;

FIG. 1C is an example of a probe of a voltmeter which is adaptable tothe fixture shown in FIG. 1B and FIG. 7B. When the probe shown in FIG.1C is inserted into receptacle 105 (106) in FIG. 1B, the probe-tip willbe inserted firmly in socket 102a (103a);

FIGS. 2A 2C are respectively a crystal unit, an equivalent circuit ofthe crystal unit and an admittance circle diagram of the crystal unit;

FIG. 3 is a circuit diagram showing one embodiment of the presentinvention;

FIGS. 4 6 are diagrams explaining the characteristics of the circuitshown in FIG. 3;

FIG. 7A is a circuit diagram showing another embodiment of the presentinvention;

FIG. 7B is a fixture for carrying out the method according to thepresent invention using the circuit diagram shown in FIG. 7A;

FIG. 7C is a lid for the shielding box shown in FIG. 78, both lid andshielding box are made of copper.

We assume firstly that an element which is purely non-reactive and whoseresistance value is known, is realizable in HF or VHF range by a certainsuitable means. As it is realized that this assumption may bequestioned, a method for its realization will be detailed hereinafter.When this assumption is realized, the following adjustment is possible.That is, connecting the above-mentioned purely non-reactive element(say, element A) in series with a circuit (say B) which is adjustable soas to become non-reactive and applying a radio frequency voltage to theseries circuit of element A and circuit B, circuit B can be adjusted sothat the phase difference between the terminal voltage V,, across theabove-mentioned series circuit and the terminal voltage V across circuitB become null by observing the above-mentioned phase difference with aninstrument such as vector voltmeter 8405A manufactured by HewlettPackard Co.

Circuit B is, as shown in FIG. 1, composed of a resistor R including astray inductance L, a variable capacitor C,, which is connected inparallel to resistor R, and a voltmeter V indicating the voltageappearing across the terminals of the above-mentioned parallel circuit.The susceptance of circuit B viewed from its terminals can be adjustedto null by adjusting variable capacitor C,, so that the sum of thecapacitances of capacitor C,, and the voltmeter compensates for theeffect of stray inductance L of resistor R.

When the above-mentioned adjustment of circuit B is carried out at acertain frequency f,,, circuit B virtually becomes non-reactive in thefrequency range lower than f provided that 21rfi,L/R is sufficientlysmall. The

resistance of circuit B can be given by the following equation,

o/ l (RA RB)/RB or 8 A/[( o/ 1) where R, and R are resistances ofresistor A and circuit B respectively.

After this adjustment, connecting a quartz crystal unit (say C) of afrequency lower than f between sockets 102 and 103 in place of resistorA, the frequency of a radio-frequency source 101 is adjusted so that twovoltages V,, and V become again in phase, and the adjusted frequencyindicates the non-reactive frequency of quartz crystal unit C. Thenon-reactive resistance R of quartz crystal unit C can be determined bythe following relation between the two voltages V, and V One arrangementof the embodiment of the abovementioned method is shown in FIG. 1B, andan example of a probe of a voltmeter which is adaptable to thearrangement is shown in FIG. 1C. Important points to be noticedconcerning the arrangement are as follows.

a. Sockets 102a and 103a for the probe-tips are directly welded orsoldered to two sockets 102 and 103 respectively.

b. A large flat copper plate 104 is provided so as to minimize thepotential differences among the following: each of two receptacles forvoltmeter-sheaths 105 and 106; outer conductor 107b of the connector tothe radio-frequency source, and; ribbon shape conductor 108 to the baseelectrode of variable capacitor C,,. In addition, a wedge shape copperplate 111 is provided between the two receptacles 105 and 106 for thesame purpose.

0. Sockets 102, 102a and 103, 103a are supported by two long insulators112 and 113 in order to minimize the capacitances between them.

d. A headless screw (not visible in FIG. 1B) is provided for theadjustment of capacitor C, from outside.

e. Frame 109 of the fixture is made of insulating material, so thatparasitically distributed capacitances between the elements of thecircuit are as small as possible.

f. A vent hole H is provided so that the interior temperature of thefixture rapidly becomes equal to the ambient temperature, particularlywhen the fixture is operated in a thermostat.

An important point which is left out of the above explanation is how anelement which is purely nonreactive and whose resistance value is knownis realized. The inventors were successful in determining thenon-reactive frequency f, and the non-reactive resistance R for any onequartz crystal unit by a method, which will be explained in detailhereinafter. Moreover, such quartz crystal unit is used as the purelynonreactive element A of this invention.

In describing the precision determination of f, and R we shall refer tothe well known equivalent network of a crystal unit and an admittancecircle, shown in FIGS. 2A 2C. The determination of the reactance ofparallel capacitance C (say X,) will be described first, and then thedetermination of the series resonant frequency f and the resistance R,of the motional arm. Next the theoretical determination of f, in termsof fl, and R,,/X will be described and, finally, the determination ofR,.

A. A method of determining the reactance X First, an explanation will begiven concerning a method of determining the reactance X,. As shown inFIG. 3, a series resonance circuit, which is composed of a coil L whoseresistance is R,, and a capacitor C is connected via a pair of sockets 2and 3 for the crystal unit undermeasurement and a ballast resistor r,,to a radio frequency source I. The ballast resistor r,, is provided onlyfor the purpose of maintaining the load more or less constant for theradio frequency source 1, and about 50 Q is selected as the value of theballast resistor r,,.

First, a short circuit piece 4 is placed between the sockets 2 and 3 forthe crystal unit and the voltage V is measured with regard to anexciting frequency f while maintaining the voltage V at a constantvalue. Then, the following equation is obtained.

V0 /j ll) d j rll where I, the current through R,,L,,C,,, is equal tojwC -V,. Then o/ V1) ll j ll ll fl 1 Therefore where If V,,/V isgraphically represented with respect to f, a V-shape curve will beobtained, and ifj instead of f, is taken for the abscissa as shown inFIG. 4, the curve becomes symmetrical with respect to the vertical axisat j /f, l V201, and the value of V,,/ V becomes equal to (a 1 4c?) theminimum value.

a, which is equal to the inverse square of the quality factor ofR,,L,,C,, circuit, is extremely small compared with 1. Accordingly, afrequency where the value V /V becomes minimum is virtually a naturalfrequency f,,. By using this relation, the capacitor C is adjusted sothat the natural frequency f, coincides with the nominal frequency ofthe crystal unit in the initial four digits.

As it is rather laborious to indicate the abscissa of FIG. 4, by a scaleof squared frequency f, the following method may actually be usedinstead.

Since it is de sirable that the quality factor Q l/VE) of the circuit RL C is selected to be a value as large as possible, we may assume thatsaid value is of the order of 100. Therefore, an impedance at afrequency which is separated a few percent from the frequency where theimpedance of this circuit becomes the minimum impedance reaches severaltimes said minimum impedance. For the purpose of coinciding thefrequency of said minimum impedance to a nominal frequency of thecrystal unit, the following method is useful. First the voltage V ismeasured at two frequencies, one of which is 4.00 percent higher thanthe nominal frequency of the crystal unit and the other of which is 4.17percent lower than the nominal frequency of the crystal unit. Thecapacitor C is then adjusted so that the voltage V, becomes equal to themean value of the two measured voltages at one of the abovementionedfrequencies. After that the voltage V, is again measured at said twofrequencies. If, now, the two values of V, are coincident, theadjustment of C, is completed. If these two values are not coincident,said adjustment of capacitor C must be continued.

After completing the above-mentioned adjustment, the short circuit piece4 is replaced with crystal unit 5, the frequency of radio frequencysource 1 is adjusted within the range of about :tlO percent of saidnominal frequency, and V is measured by keeping V constant. This isshown in FIG. 5. The following equation can then be obtained except foraportion near the series resonance frequency f, of the motional arm ofthe crystal unit.

0 /j 1 1 'j a+( /j a)l where 1 =jwC V, as stated earlier; and C 1 is theparallel capacitance, the inductance of the lead wires from theterminals to the blank of the crystal being taken into account.

Rearranging the above equation and neglecting R results in Since thisequation shows that V,,/ V, is linear with respect to 00 the curve ofV,,/ V, tends to a straight line as shown by a broken straight line.This means that the broken straight line shows the relation between V,,/V, and f provided that the motional arm of the unit is omitted from thecircuit. Moreover, since L C is already tuned to the nominal frequencyof the unit,

(1) L C l I Consequently, at the nominal frequency of the crystal unit,

0/ VI 41/ 1 I d i where X, l/(21rf,,C X,, l/(2'nf,,C, and f,, is thenominal frequency.

By introducing a measured value of capacitor C the value of X can bedetermined.

Also in the case of FIG. 5, when it is desired to avoid thelaboriousness of representing the abscissa by a scale of squaredfrequency, the values of V,,/V can be measured at two frequencies of theexciting source, one of which is 10.00 percent higher than the nominalfrequency of the crystal unit and the other of which is 11.12 percentlower than the nominal frequency, and then the mean of the two values ofV,,/V at the two frequencies is equal to C /C, or X,/X

B. A method of determining the series resonant frequency f,, theresistance R,,, etc.

A method of determining the natural frequency f,,, the resistance R,,,etc., of the motional arm of the crystal unit will next be explained. Anoutline of this method was already made known in the 24th AnnualFrequency Control Symposium held in Atlantic City, N.J., in April, 1970.

As explained already by using FIG. 3, we firstly tune L C to the nominalfrequency of the crystal unit. The quality factor Q of the circuit R L Cis of the order of several hundred at the most, and, on the other hand,the operating frequency range for a crystal unit is extremely narrow.Hence, if the natural frequency f, is adjusted to be in coincidence withthe nominal frequency of the unit, the entire circuit including the unitis equivalent to the case where only the resistance R,,, is in serieswith the unit, when viewed from the terminals of voltmeter V The currentthrough the capacitor C, is virtually equal to 21rf,C, V or V,/X where Vis the terminal voltage across the capacitor C,,. Thus the followingrelation holds at any frequency f of exciting voltage V V, 27rfC V,Z,where Z is the impedance of the unit including the series resistanceR,,. 7

Transformation of the last equation results in FIG. 6 shows the relationbetween (V V with reference to f.

The locus y, obtained by plotting the central points between the twopoints corresponding to various values of (V /V0 becomes a branch of ahyperbola. When the curvature of this locus y is not small, a straightline y is very useful. y is drawn by plotting values of y multiplied byb/(b-y), where b= (X /X The two curves y and y cross at a point on thehorizontal line which is situated at the height of (R /X from the axisf, (for the sake of convenience, we call it elevated frequency axis").

This intersection point of y to the elevated frequency axis gives theseries resonant frequency fi, of the motional arm.

Generally, R is very small compared with R and in such a case, theelevated frequency axis is very close to the frequency axis, and theintersecting points of y with the frequency axis and the elevatedfrequency axis make no difference in f.,. If the locus y is virtually astraight line, y can, of course, be dispensed with.

Next, the inclination 6 of the locus y is estimated from the graph ofFIG. 6. Then the frequency f, where the crystal unit becomes purelynon-reactive is given by the following equation.

When the frequency of the radio frequency source is set to the value off, that is given in the abovementioned equation, the non-reactiveresistance R, is given by V,)X,, at this frequency f Another embodimentof the present invention will next be explained. With respect to acrystal unit of VHF, it is preferable to use the following improvedmethod. This is because the short circuit piece 4 in FIG. 3, used atfirst during tuning of the circuit R L C to the frequency of the crystalunit, cannot be sufficiently non-reactive. Accordingly, the replacementof this short circuit piece with the crystal unit does not rigorouslymean that the total circuit is exactly equal to the crystal unit plus RTherefore, it is preferable to use a fixture as shown in FIGS. 7Athrough 7C. Referring to FIGS. 7A and 7B, the fixture of the presentinvention comprises a high frequency source 1, a pair of soekets 6 and 7where the crystal unit and a connecting piece 8 are alternatelyinserted, and a pair of sockets 6a and 7a, into one of which theprobe-tip of a voltmeter is inserted. The sockets 6 and 7 are welded orsoldered to the sockets 6a and 7a respectively. In the above-mentionedarrangement, when the sheath of the probe is inserted into thereceptacle 9, a tip of the probe is actually in contact with one of theterminals of the crystal unit. The receptacles 9 and 10 for the sheathsof voltmeters are welded or soldered together at the position nearestthe terminals 6 and 7, and also welded or soldered to a copper plate 13.A headless screw (not visible in FIG. 7B) is provided for the adjustmentof capacitor C, from the outside.

Large flat copper plate 13 is provided in order to minimize thepotential differences among the following: each of the two receptacles 9and I0; outer conductor 11b of the connector to the radio-frequencysource and; ribbon shape conductor 13a to the base electrode of variablecapacitor C In addition, a wedge shape copper plate 17 is providedbetween the two receptacles 9 and 10 for the same purpose. Sockets 6, 6aand 7, 7a are supported by long insulators l8 and 19 in order tominimize the capacitance between them.

The circuit L C is enclosed by a shield box 14 together with its lid 15shown in FIG. 7C in order to minimize mutual induction between internalobjects of the shield box and external objects. Vent holes 16 shown inFIGS. 78 and 7C are provided on the shield box 14 and its lid 15 so thatthe interior temperatures of the fixture rapidly become equal to theambient temperature, particularly when the fixture is operated in athermostat.

For the measurement of various constants of the crystal unit withabove-mentioned fixture, the connecting piece 8 is first connectedbetween sockets 6 and 7, and the probe-tip of a voltmeter is insertedinto the receptacle 10 so as to observe the voltage V,,, and anothervoltmeter is connected to the terminals 12a and 12b for the purpose ofobserving the voltage V A radio frequency source is connected to 11a and11b. By adjusting the value of C following the procedure alreadydescribed with reference to FIG. 3, the circuit R L C is tuned to thenominal frequency of the crystal unit. In this case, the role of theconnecting piece is different from the short circuit piece 4 in FIG. 3,because the connecting piece is only to make the path from the source tothe circuit R L C When the connecting piece 8 is replaced by the crystalunit 5, the probe of the voltmeter is moved from the receptacle I0 to 9,and then V exactly indicates the total voltage across the crystal unitplus the whole cir- CLIlI RdL ICd.

By following the above-mentioned procedure, the reactance of aconnecting piece itself can also be determined. A typical example of thereactance value of the connecting piece which was determined by theabovementioned procedure was 2.6 Q at MHz. This value is not negligiblysmall, because said value causes an error on the order of 0.5 X 10 for fof a crystal unit in the range of 100 MHZ.

What is claimed is:

1. A method of measuring parameters of crystal units comprising,

a. determining a non-reactive frequency of a crystal unit (say A) whichmay be freely selected from a plurality of crystal units to be tested,

b. applying radio frequency voltage to the series circuit (say A B)composed of the crystal unit (A) and a circuit (say B) which isadjustable to nonreactive resistance at the non-reactive frequency ofthe crystal unit (A),

c. adjusting the reactance of the circuit (B) to be non-reactive withrespect to said non-reactive frequency of the crystal unit (A) so thatthe phase of the voltage across the series circuit (A B) and the phaseof the voltage across the circuit (B) coincide,

d. replacing the crystal unit (A) by a crystal (say C) which is selectedfrom the remainder of said plurality of crystal units,

e. applying radio frequency voltage to the series circuit (C B) andadjusting the frequency of applied voltage so that the phase of voltageacross the series circuit (C B) coincides with the phase of voltageacross the circuit (B), and

f. adopting the reading of frequency thus adjusted as the non-reactivefrequency of the crystal unit (C).

the circuit (B) and the resistance of the circuit (B).

1. A method of measuring parameters of crystal units comprising, a.determining a non-reactive frequency of a crystal unit (say A) which maybe freely selected from a plurality of crystal units to be tested, b.applying radio frequency voltage to the series circuit (say A + B)composed of the crystal unit (A) and a circuit (say B) which isadjustable to non-reactive resistance at the nonreactive frequency ofthe crystal unit (A), c. adjusting the reactance of the circuit (B) tobe non-reactive with respect to said non-reactive frequency of thecrystal unit (A) so that the phase of the voltage across the seriescircuit (A + B) and the phase of the voltage across the circuit (B)coincide, d. replacing the crystal unit (A) by a crystal (say C) whichis selected from the remainder of said plurality of crystal units, e.applying radio frequency voltage to the series circuit (C + B) andadjusting the frequency of applied voltage so that the phase of voltageacross the series circuit (C + B) coincides with the phase of voltageacross the circuit (B), and f. adopting the reading of frequency thusadjusted as the nonreactive frequency of the crystal unit (C).
 2. Amethod of measuring parameters of crystal units (C) according to claim1, comprising further determining the non-reactive resistance of thecircuit (B) at said non-reactive frequency of the crystal unit (A), fromthe ratio of the voltage across the series circuit (A + B) and thecircuit (B), and determining the non-reactive resistance of the crystal(C) from the ratio of the voltage across the series circuit (C + B) andthe voltage across the circuit (B) and the resistance of the circuit(B).